The Ontic Closure Theorem

established that Obj(τ) is ontically sealed: five pairwise disjoint sets, countable, with unique representation. We now prove two culminating theorems that complete Part II. The Rigidity Theorem shows that τ admits no non-trivial automorphisms: Aut(τ) = {id}. Every element of τ is uniquely determined by its structural position, not by its name. The Categoricity Theorem shows that τ₀ has a unique model up to isomorphism: any two structures satisfying K1–K6 are isomorphic via a unique isomorphism. Together, these results establish that τ is not merely a model of τ₀ but the model. The ontic seal is now absolute.